SOLUTION: The hypotinuse of a right triangle is 8cm long. One leg is 2 cm longer than the other. find the length of the longer leg to the nearest tenth. Thank you

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Question 40361: The hypotinuse of a right triangle is 8cm long. One leg is 2 cm longer than the other. find the length of the longer leg to the nearest tenth.
Thank you
Answer by Nate(3500) About Me  (Show Source):
You can put this solution on YOUR website!
One leg = z
Other leg = x
Equation:
z+%2B+2+=+x
Use pythagorus formula:
a%5E2+%2B+b%5E2+=+c%5E2
z%5E2+%2B+x%5E2+=+8%5E2
z%5E2+%2B+%28z+%2B+2%29%5E2+=+64
z%5E2+%2B+z%5E2+%2B+4z+%2B+4+=+64
2z%5E2+%2B+4z+-+60+=+0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B4x%2B-60+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%284%29%5E2-4%2A2%2A-60=496.

Discriminant d=496 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-4%2B-sqrt%28+496+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%284%29%2Bsqrt%28+496+%29%29%2F2%5C2+=+4.56776436283002
x%5B2%5D+=+%28-%284%29-sqrt%28+496+%29%29%2F2%5C2+=+-6.56776436283002

Quadratic expression 2x%5E2%2B4x%2B-60 can be factored:
2x%5E2%2B4x%2B-60+=+2%28x-4.56776436283002%29%2A%28x--6.56776436283002%29
Again, the answer is: 4.56776436283002, -6.56776436283002. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B4%2Ax%2B-60+%29

z is about 4.6
x is about 6.6